GA_Opioid_Report
Hayoung Jung
Import Libraries and Data
Data Structure and Summary Table
## Rows: 159
## Columns: 30
## $ NAME <chr> "Rabun", "Towns", "Fannin", "Murray", "Whitf…
## $ FIPS <chr> "13241", "13281", "13111", "13213", "13313",…
## $ county <chr> "241", "281", "111", "213", "313", "047", "2…
## $ rucc_code13 <fct> non, non, non, sm, sm, mm, non, mm, mm, non,…
## $ rucc_code13_n <dbl> 6, 6, 6, 4, 4, 3, 6, 3, 3, 6, 5, 6, 6, 5, 5,…
## $ mortality <dbl> 4, 3, 5, 6, 15, 10, 2, 13, 4, 6, 10, 8, 7, 7…
## $ population <dbl> 16602, 11506, 25322, 39782, 104658, 66550, 2…
## $ Year <dbl> 2020, 2020, 2020, 2020, 2020, 2020, 2020, 20…
## $ state <chr> "13", "13", "13", "13", "13", "13", "13", "1…
## $ pct_poverty <dbl> 13.6, 8.9, 7.6, 11.8, 11.3, 7.2, 12.1, 10.4,…
## $ vacancy_rate <dbl> 44.6, 39.6, 36.1, 10.3, 9.5, 8.8, 31.1, 13.6…
## $ unemployment_rate <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ unemployment_rate_out <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ pct_black <dbl> 2.0, 1.8, 0.8, 1.3, 4.5, 3.7, 1.0, 5.2, 2.1,…
## $ dist_to_usroad <dbl> 177343.881, 229218.710, 177629.928, 65168.05…
## $ dist_to_treatment <dbl> 100811.3814, 63782.7232, 79264.3957, 4003.75…
## $ incidence <dbl> 2.409348e-04, 2.607335e-04, 1.974568e-04, 1.…
## $ mort_rate <dbl> 0.24093483, 0.26073353, 0.19745676, 0.150821…
## $ Name <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ Name_Seat <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ pct_poverty_std <dbl> -0.15651142, -0.98484701, -1.21396111, -0.47…
## $ vacancy_rate_std <dbl> 3.08075917, 2.51252486, 2.11476084, -0.81732…
## $ unemployment_rate_std <dbl> -0.74498218, -0.70715012, -0.10183723, 0.162…
## $ unemployment_rate_out_std <dbl> -0.793303461, -0.751995315, -0.091064977, 0.…
## $ pct_black_std <dbl> -1.5609990, -1.5723595, -1.6291621, -1.60076…
## $ dist_to_usroad_std <dbl> 0.92635695, 1.52090721, 0.92963541, -0.35931…
## $ dist_to_treatment_std <dbl> 1.211776760, 0.425387080, 0.754176404, -0.84…
## $ rucc_code13_4 <fct> mi_non, mi_non, mi_non, mm_sm, mm_sm, mm_sm,…
## $ rucc_code13_5 <fct> mi_non, mi_non, mi_non, sm, sm, mm, mi_non, …
## $ geometry <MULTIPOLYGON [US_survey_foot]> MULTIPOLYGON (((88…| Characteristic | Overall N = 1591 |
Mortality rate
|
p-value2 | ||
|---|---|---|---|---|---|
| Low N = 591 |
Moderate N = 611 |
High N = 391 |
|||
| Rural-Urban Continuum Code | 0.008 | ||||
| Large Central Metro & Large Fringe Metro | 29 (18%) | 5 (8.5%) | 18 (30%) | 6 (15%) | |
| Medium Metro | 15 (9.4%) | 3 (5.1%) | 10 (16%) | 2 (5.1%) | |
| Small Metro | 30 (19%) | 15 (25%) | 8 (13%) | 7 (18%) | |
| Micropolitan & Non-Metro | 85 (53%) | 36 (61%) | 25 (41%) | 24 (62%) | |
| Mortality Count | 3 (1, 8) | 1 (0, 2) | 5 (2, 14) | 6 (4, 9) | <0.001 |
| County Population | 22,736 (11,319, 57,089) | 21,498 (10,343, 43,014) | 27,113 (17,277, 91,600) | 20,533 (12,830, 35,871) | 0.040 |
| Poverty rate | 14.0 (10.1, 18.1) | 16.6 (12.7, 20.0) | 11.7 (8.7, 16.6) | 13.8 (10.0, 17.0) | 0.002 |
| Vacancy rate | 16 (12, 21) | 16 (14, 22) | 14 (10, 19) | 19 (12, 27) | 0.042 |
| Unemployment rate | 5.70 (4.30, 7.10) | 5.80 (4.20, 8.60) | 5.60 (4.70, 6.50) | 5.40 (4.20, 6.60) | 0.5 |
| Percentage of Black Population | 29 (17, 41) | 31 (25, 47) | 25 (12, 36) | 30 (11, 41) | 0.012 |
| Distance to interstate | 83,373 (21,222, 136,712) | 90,371 (47,267, 151,962) | 63,821 (10,797, 105,001) | 95,523 (39,523, 149,321) | 0.035 |
| Unknown | 2 | 1 | 1 | 0 | |
| Distance to treatment | 19,036 (3,692, 83,602) | 14,239 (3,721, 90,642) | 21,738 (4,079, 82,826) | 16,063 (2,889, 83,596) | 0.8 |
| Unknown | 2 | 1 | 1 | 0 | |
| 1 n (%); Median (Q1, Q3) | |||||
| 2 Fisher’s exact test; Kruskal-Wallis rank sum test | |||||
- This table presents an analysis of difference among low, moderate,
and high mortality rate groups across various demographic,
socioeconomic, and geographic factors. Significant disparities were
found in rural-urban continuum code (p=0.008), county population
(p=0.040), poverty rate (p=0.002), vacancy rate (p=0.042), percentage of
black population (p=0.012), and distance to interstate (p=0.035). These
variablees differ meaningfully across mortality rate groups, suggesting
potential associations with mortality outcomes.
- Counties that are missing distance to interstate and treatment are Columbia and Echols.
Exploratory Data Analysis
1. NAME
Name of the county
- There are 159 counties in Georgia.
2 & 3. FIPS code / Code
FIPS code
- All FIPS codes begin with ‘13’, which represents Georgia’s state code, followed by the specific county codes.
4 & 5. rucc_code13 / rucc_code13_n
Rural-urban continuum code of the County
- Most counties in Georgia are non-metro, followed by small metro,
large fringe metro, micropolitan, and medium metro areas.
Only Fulton county is classified as a large central metro. - Most major metro areas, including large central metro, large fringe metro, and medium metro areas, are concentrated in the northern part of the state, particularly around Atlanta.
6 & 7. mortality / population
The number of opioid-related deaths and population in each county
| NAME | mortality |
|---|---|
| Fulton | 127 |
| Cobb | 117 |
| Gwinnett | 94 |
| DeKalb | 80 |
| Richmond | 54 |
| NAME | population |
|---|---|
| Fulton | 1041423 |
| Gwinnett | 920260 |
| Cobb | 755754 |
| DeKalb | 753253 |
| Chatham | 290501 |
- Mortality counts are concentrated in urban areas, meaning higher counts are typically found in areas with large populations, such as Fulton, Gwinnett, Cobb, and Dekalb counties.
- In southern Georgia, Tift County stands out with a relatively high count (31), suggesting a higher expected mortality rate.
8. mort_rate
Mortality rate = mortality count/population in each county
- U.S. Census Bureau, “tl_2020_13_prisecroads”, TIGER/Line Shapefiles, 2020, https://www.census.gov/cgi-bin/geo/shapefiles/index.php?year=2020&layergroup=Roads, accessed on October 2, 2024.
| NAME | incidence |
|---|---|
| Turner | 0.0010049 |
| Tift | 0.0007636 |
| Randolph | 0.0005654 |
| Telfair | 0.0005629 |
| Wilkinson | 0.0005581 |
- Located in southern and central Georgia, Turner County has the highest mortality rate at 0.001, followed by Tift (0.0008), Randolph (0.0006), Telfair (0.0006), and Wilkinson (0.0006) counties, which are also in the southern part of the st
- We aim to identify whether certain covariates in counties are associated with higher or lower mortality rates. On each covariate map, we are looking for emerging patterns across these areas.
The following are summary of the geographic distribution of the covariates that we are interested in.
9. pct_poverty
Percentage of people whose income in the past 12 months is below the poverty level in each county
| NAME | pct_poverty |
|---|---|
| Taylor | 28.6 |
| Taliaferro | 28.5 |
| Terrell | 28.0 |
| Jenkins | 27.5 |
| Seminole | 27.1 |
- Taylor County has the highest poverty rate at 28.6%, followed by Taliaferro (28.5%), Terrell (28.0%), Jenkins (27.5%), and Seminole (27.1%) counties.
- Overall, counties in southern and central Georgia tend to have relatively higher poverty rates compared to those in northern Georgia.
10. vacancy_rate
Percentage of housing vacancy in each county
| NAME | vacancy_rate |
|---|---|
| Quitman | 53.2 |
| Rabun | 44.6 |
| Hancock | 43.3 |
| Towns | 39.6 |
| Clay | 39.2 |
- Quitman County has the highest vacancy rate at 53.2%, followed by Rabun (44.6%), Hancock (43.3%), Towns (39.6%), and Clay (39.2%) counties.
- Vacancy rates vary widely across the state, with high rates observed in northern, central-eastern, and southern Georgia.
11 & 12. unemployment_rate / _out
Unemployment rate (before / after treating outliers) in each county
- Quitman county has a notably high unemployment rate of 21.4%, making it an outlier among other counties. To address this outlier, we replaced any values above the 99th percentile with the 99th percentile of the ranked value.
| NAME | unemployment_rate_out |
|---|---|
| Quitman | 13.826 |
| Baker | 13.826 |
| Charlton | 13.700 |
| Long | 12.400 |
| Crisp | 12.000 |
- After adjusting for outliers, Quitman and Baker counties have the highest unemployment rate at 13.83%, followed by Charlton (13.7%), Long (12.4%), and Crisp (12%) counties.
- Overall, counties in southern and rural Georgia tend to have higher unemployment rates compared to those in northern Georgia.
13. pct_black
Percentage of county population that is made up of Black people
| NAME | pct_black |
|---|---|
| Hancock | 72.7 |
| Clayton | 72.5 |
| Dougherty | 71.2 |
| Randolph | 64.4 |
| Macon | 62.6 |
- Hancock County has the largest percentage of Black population at 72.7%, followed by Clayton (72.5%), Dougherty (71.2%), Randolph (64.4%), and Macon (62.6%) counties.
- In general, counties with higher percentages of Black populations are more common in central and southwestern Georgia.
14. dist_to_usroad
Distance from County Seat to Interstate
| NAME | dist_to_usroad |
|---|---|
| Seminole | 446751.5 |
| Miller | 388135.0 |
| Early | 371694.7 |
| Decatur | 364239.2 |
| Bacon | 313541.7 |
- Seminole County has the longest distance from the county seat to the interstate at 446,752 feet, followed by Miller (338,135 feet), Early (371,695 feet), Decatur (364,239 feet), and Bacon (313,542 feet) counties.
- Counties in southwestern and southeastern Georgia tend to have longer distances to interstates, particularly in more rural areas.
15. dist_to_treatment
Distance to Treatment Centers
- U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Behavioral Health Services Information System. (2024). FindTreament_Facility_listing. Retrieved from https://findtreatment.gov/locator.
| NAME | dist_to_treatment |
|---|---|
| Quitman | 185131.5 |
| Warren | 164829.7 |
| Stewart | 161330.9 |
| Glascock | 160496.1 |
| Randolph | 153486.9 |
- Quitman County has the longest distance to treatment centers at 185,132 feet, followed by Warren (164,830 feet), Stewart (161,331 feet), Glascock (160,496 feet), and Randolph (153,437 feet) counties.
- Counties in southwestern and rural central Georgia generally have longer distances to treatment centers.
Check the Distribution of Covariates
pct_poverty
vacancy_rate
unemployment_rate_out
pct_black
dist_to_usroad
dist_to_treatment
Poisson Random Intercept Model with a Population Offset
\[
y_i|\mu_i \sim \text{Poisson}(\mu_i), \\ where \ \mu_i = E(y_i) =
Var(y_i)
\\\
\\
log(\frac{\mu_i}{pop_i}) = \beta_0 + \beta_1\,poverty\_rate_i +
\beta_2\,vacancy\_rate_i + \beta_3\,unemployment\_rate_i +
\beta_4\,pct\_black_i + \beta_5\,dist\_to\_road_i +
\beta_6\,dist\_to\_treatment_i + \theta_i
\\\
\\
log(\mu_i) = log\,pop_i + \beta_0 + \beta_1\,poverty\_rate_i +
\beta_2\,vacancy\_rate_i + \beta_3\,unemployment\_rate_i +
\beta_4\,pct\_black_i + \beta_5\,dist\_to\_road_i +
\beta_6\,dist\_to\_treatment_i + \theta_i
\\\
\\
\theta_i \sim N(0,\tau^2)
\]
\(y_i\) : mortality count for county i
\(\mu_i\) : expected mortality count for county i
\(log\,pop_i\) : population of county i, used as an offset to adjust for the different population sizes across the counties
\(\beta_0\) : baseline log expected mortality rate
\(\theta_i\) : random intercept for county i, county-specific deviation in baseline log expected mortality rate
\(e^{\beta_1}\) : relative mortality rate change for a one standard deviation increase in the poverty rate
\(e^{\beta_2}\) : relative mortality rate change for a one standard deviation increase in the vacancy rate
\(e^{\beta_3}\) : relative mortality rate change for a one standard deviation increase in the unemployment rate
\(e^{\beta_4}\) : relative mortality rate change for a one standard deviation increase in the percentage of black population
\(e^{\beta_5}\) : relative mortality rate change for a one standard deviation increase in the distance to the interstate
\(e^{\beta_6}\) : relative mortality rate change for a one standard deviation increase in the distance to the treatment center
Fit the Model
# Fit the poisson regression model
dat$log_pop = log(dat$population)
fit = glmer(mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +
unemployment_rate_out_std + pct_black_std + dist_to_usroad_std +
dist_to_treatment_std + (1|county),
family = poisson(link = "log"), data = dat)
summary(fit)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +
## unemployment_rate_out_std + pct_black_std + dist_to_usroad_std +
## dist_to_treatment_std + (1 | county)
## Data: dat
##
## AIC BIC logLik deviance df.resid
## 753.0 777.5 -368.5 737.0 149
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.34923 -0.54256 -0.04798 0.37666 2.74739
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.1948 0.4413
## Number of obs: 157, groups: county, 157
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.93104 0.06266 -142.541 <2e-16 ***
## pct_poverty_std 0.01450 0.07978 0.182 0.8558
## vacancy_rate_std 0.15993 0.07527 2.125 0.0336 *
## unemployment_rate_out_std -0.13974 0.07645 -1.828 0.0676 .
## pct_black_std -0.07285 0.06573 -1.108 0.2677
## dist_to_usroad_std -0.17990 0.07779 -2.313 0.0207 *
## dist_to_treatment_std 0.03392 0.07356 0.461 0.6447
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pct_p_ vcnc__ unm___ pct_b_ dst_t_s_
## pct_pvrty_s 0.087
## vcncy_rt_st 0.026 -0.320
## unmplymn___ 0.086 -0.189 0.126
## pct_blck_st -0.016 -0.402 0.045 -0.343
## dst_t_srd_s 0.181 -0.247 -0.315 -0.004 0.183
## dst_t_trtm_ 0.200 -0.066 -0.356 -0.080 0.047 0.004The baseline relative mortality rate is \(e^\hat{\beta_0}\) = \(e^{-8.93}\) = 0.0001.
There exists heterogeneity in baseline mortality rate with a between-county standard deviation \(\tau\) of 0.44.
So 95% of the counties have baseline mortality rates between \(e^{-8.93 \pm 1.96 \times 0.44}\) = (0.00006, 0.0003).There is evidence that mortality rate increases by approximately 17.4% (\(e^\hat{\beta_2}\) = \(e^{0.16}\) = 1.174) for a one standard deviation increase in the vacancy rate.
There is evidence that mortality rate decreases by approximately 16.5% (\(e^\hat{\beta_5}\) = \(e^{-0.180}\) = 0.835) for a one standard deviation increase in the distance to the interstate.